How do I convert radians to degrees?

To convert radians to degrees, multiply by 180/π (approximately 57.2958). For example, π radians × 180/π = 180°. π/2 rad = 90°, π/3 rad = 60°, π/4 rad = 45°.

What is the formula for radians to degrees?

degrees = radians × (180 / π). Since π radians = 180°, multiply radians by 180/π to get degrees. In code: radians * 180 / Math.PI. 1 radian ≈ 57.2958 degrees.

How many degrees is 1 radian?

1 radian = 57.2958° (approximately 57.3°). This is about 57° 17' 45". One radian is the angle where the arc length equals the radius of the circle.

How many radians is 1 degree?

1° = 0.0174533 radians = π/180 rad. This is a very small angle. At 1 km distance, 1° spans about 17.5 meters. There are 360° in a circle vs 2π radians.

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Radians to Degrees Converter

Convert radians (rad) to degrees (°) with this easy-to-use angle converter.

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External Resources

Wikipedia: Radian Wikipedia: Degree (angle)NIST: Metric System

Frequently Asked Questions

How do I convert radians to degrees?: To convert radians to degrees, multiply by 180/π (approximately 57.2958). For example, π radians × 180/π = 180°. π/2 rad = 90°, π/3 rad = 60°, π/4 rad = 45°.
What is the formula for radians to degrees?: degrees = radians × (180 / π). Since π radians = 180°, multiply radians by 180/π to get degrees. In code: radians * 180 / Math.PI. 1 radian ≈ 57.2958 degrees.
How many degrees is 1 radian?: 1 radian = 57.2958° (approximately 57.3°). This is about 57° 17' 45". One radian is the angle where the arc length equals the radius of the circle.
How many radians is 1 degree?: 1° = 0.0174533 radians = π/180 rad. This is a very small angle. At 1 km distance, 1° spans about 17.5 meters. There are 360° in a circle vs 2π radians.
What is a radian and why use it?: A radian is the SI unit of angle where 1 radian = arc length / radius. Radians make calculus natural: d/dx sin(x) = cos(x) only when x is in radians. Radians simplify arc length (s = rθ), sector area (A = ½r²θ), and angular velocity (ω = θ/t).
How do I convert radians to degrees in JavaScript?: Use: degrees = radians * 180 / Math.PI. Example: Math.atan2(y, x) returns radians, convert: Math.atan2(1, 0) * 180 / Math.PI = 90°. For display, convert radian output to degrees for readability.
What is the radians to degrees conversion for 2π?: 2π rad = 360°. This is a full circle. 2π appears everywhere in physics: the circumference formula C = 2πr, angular frequency ω = 2πf, and trigonometric functions have period 2π.
What is the radians to degrees conversion for π/2?: π/2 rad = 90° (right angle). This is a quarter circle. sin(π/2) = 1, cos(π/2) = 0. Used extensively: perpendicular lines, coordinate axes, vector dot products.
What is the radians to degrees conversion for π/4?: π/4 rad = 45°. Common: isometric angles, diagonal of a square, diagonal of a rectangle. sin(π/4) = cos(π/4) = √2/2 ≈ 0.7071. Popular in design and photography composition.
How do I memorize common radian to degree conversions?: 0 rad = 0°, π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, 2π/3 = 120°, 3π/4 = 135°, 5π/6 = 150°, π = 180°, 3π/2 = 270°, 2π = 360°. These correspond to unit circle angles.
What is the radians to degrees conversion for π/6?: π/6 rad = 30°. Key triangle: 30-60-90 with sides 1:√3:2. sin(π/6) = 0.5, cos(π/6) = √3/2 ≈ 0.8660. Used in hexagonal geometry and 30° drafting triangles.
How do I convert radians to degrees for GPS and navigation?: GPS calculations use radians in formulas (haversine, Vincenty), but display degrees. Convert radian lat/lon to degrees for readability. 1 radian latitude = about 57.3° or 6,371 km on Earth's surface.
What is the difference between radians and degrees in math?: Degrees: 360° base-60 system from Babylonians. Radians: 2π base-π system. Calculus, advanced trig, and Fourier transforms use radians. Most people understand degrees, but all serious math uses radians.
What is the radians to degrees conversion for π?: π rad = 180°. This is a half circle (straight line). π is one of the most important constants. Euler's identity: e^(iπ) + 1 = 0. sin(π) = 0, cos(π) = -1.
How do I convert radians to degrees for trig functions?: Trig functions in math libraries take radians. To find the angle in degrees: convert asin(), acos(), atan() results from radians to degrees. Example: asin(0.5) = π/6 = 30°.
What is the radians to degrees conversion for 1.57 radians?: 1.57 rad ≈ 89.95° ≈ 90°. This is approximately π/2. Common: 1.57 rad is used as an approximation for π/2 in code comments, but use Math.PI/2 for precision.
How do I convert radians to degrees for physics?: Physics results: angular frequency ω (rad/s) × 180/π = degrees/s. Phase angles from complex numbers in radians convert to degrees for phasor diagrams. Wave equations use radians naturally.
What is the radians to degrees conversion for 3π/2?: 3π/2 rad = 270°. This is three-quarters of a circle. sin(3π/2) = -1, cos(3π/2) = 0. Used in 3D rotation matrices and polar coordinate plots.
How do I convert radians to degrees for computer graphics?: Most graphics APIs (WebGL, DirectX, Vulkan) use radians internally but often accept degrees in higher-level frameworks. CSS transform: rotate(45deg). Three.js: either. rotation.set(0, Math.PI/4, 0).
What is the radians to degrees conversion for 0.7854 radians?: 0.7854 rad ≈ 45°. This is approximately π/4. When you see 0.7854 in code, it is likely π/4. Common in rotation examples for 45-degree angles.
How do I convert radians to degrees for surveying?: Surveying uses degrees, minutes, seconds (DMS). Convert radian results: multiply by 180/π, then convert decimal degrees to DMS. 1° = 60', 1' = 60". Traverse calculations start in degrees but may use radians internally.
What is the history of the radian?: The concept of measuring angles by arc length was used by Islamic mathematicians. Roger Cotes (1714) first used the radian measure explicitly. Leonhard Euler popularized it, and the term "radian" was coined by James Thomson in 1870s.
What is the radians to degrees conversion for 2.0944 radians?: 2.0944 rad ≈ 120°. This is 2π/3. Used in 3-phase electrical systems (120° phase difference between phases). Also appears in hexagonal close-packed crystal structures.
How do I convert radians to degrees in Python?: Python: import math; degrees = math.degrees(radians). Or manually: degrees = radians * 180 / math.pi. NumPy: numpy.rad2deg(array). Use degrees for display, radians for computation.
What is the radians to degrees conversion for 0.5236 radians?: 0.5236 rad ≈ 30°. This is π/6. Common in 30-60-90 triangle calculations. Also appears in clock face: 1 hour = 30° = π/6 rad. Used in hexagonal grid systems.
How do I convert radians to degrees for astronomy?: Astronomy: angular separation in radians × 180/π = degrees. Small-angle formula: angular size (arcseconds) = (actual size / distance) × 206,265. 1 radian = 206,265 arcseconds. Parallax angles are in arcseconds.
What is the radians to degrees conversion for 4.7124 radians?: 4.7124 rad ≈ 270° = 3π/2. This is the bottom of the unit circle. sin(3π/2) = -1. Used in polar coordinates for downward direction. Common in 3D game development for downward vectors.
How do I convert radians to degrees for the haversine formula?: Haversine: a = sin²(Δlat/2) + cos(lat1)·cos(lat2)·sin²(Δlon/2). Input coordinates in radians! Convert decimal degree coordinates to radians first. Output bearing in radians, convert to degrees for compass bearing.
What is the radians to degrees conversion for 1.0472 radians?: 1.0472 rad ≈ 60° = π/3. Equilateral triangle interior angle = 60°. sin(π/3) = √3/2 ≈ 0.8660. 60° appears in hexagonal geometry, isometric grids, and equilateral triangles.
What is the radians to degrees conversion for 6.2832 radians?: 6.2832 rad ≈ 360° = 2π. Full circle. 2π rad = 360°. This is the period of sine and cosine functions. In numerical computing, angles are often normalized modulo 2π to the range [0, 2π) or (-π, π].
How do I remember the radian-to-degree conversion factor?: Remember: π = 180°. So multiply by 180/π. Common: if you see a radian value, multiply by 57.3 for degrees. If you see a degree value, multiply by 0.01745 for radians. Practice: 1 rad = 57.3°, 2 rad = 114.6°, 3 rad = 171.9°.